B. Reed

Publications252
h-index46
Citations10,211
Highly Influential Citations1,016
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  • Publications
  • Influence
A Critical Point for Random Graphs with a Given Degree Sequence
  • M. Molloy, B. Reed
  • Mathematics, Computer Science
  • Random Struct. Algorithms
  • 1 March 1995
Given a sequence of nonnegative real numbers λ0, λ1… which sum to 1, we consider random graphs having approximately λi n vertices of degree i. Essentially, we show that if Σ i(i - 2)λi > 0, then such… Expand
  • 2,005
  • 133
  • PDF
Graph Colouring and the Probabilistic Method
The term Probabilistic Method refers to the proof of deterministic statements using probabilistic tools. The method has been successfully applied to a number of problems in the field of graph… Expand
  • 397
  • 52
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
  • M. Molloy, B. Reed
  • Mathematics, Computer Science
  • Comb. Probab. Comput.
  • 1 September 1998
TLDR
We show that if ∑i(i−2)λi<0 then the graph a.s. has a giant component, and that the structure of the graph remaining after deleting C is basically that of a random graph with n′=n−∣C∣ vertices. Expand
  • 721
  • 49
  • PDF
Mick gets some (the odds are on his side) (satisfiability)
  • V. Chvátal, B. Reed
  • Mathematics, Computer Science
  • Proceedings., 33rd Annual Symposium on…
  • 24 October 1992
TLDR
Consider a randomly generated boolean formula F (in the conjunctive normal form) with m clauses of size k over n variables; k is fixed at any value greater than 1, but n tends to infinity and m = (1 + o(1))cn for some c depending only on k. Expand
  • 357
  • 41
  • PDF
Finding odd cycle transversals
TLDR
We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle transversal of order at most k, for any fixed k. Expand
  • 352
  • 36
A Bound on the Strong Chromatic Index of a Graph,
  • M. Molloy, B. Reed
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1 March 1997
TLDR
We show that the strong chromatic index of a graph with maximum degree�; is at most (2��)�2, for some�>0. Expand
  • 136
  • 36
Acyclic Coloring of Graphs
TLDR
A vertex coloring of a graph G is called acyclic if no two adjacent vertices have the same color and there is no two-colored cycle. Expand
  • 222
  • 28
  • PDF
Further algorithmic aspects of the local lemma
Copyright © 1998 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided… Expand
  • 196
  • 26
Finding approximate separators and computing tree width quickly
  • B. Reed
  • Mathematics, Computer Science
  • STOC '92
  • 1 July 1992
TLDR
We show that for any fixed <italic>k</italic>, there is a linear-time algorithm which gives an approximate separator algorithm for determining if a graph has a tree decomposition of width at most k. Expand
  • 216
  • 17
Paths, Stars and the Number Three
  • B. Reed
  • Mathematics, Computer Science
  • Comb. Probab. Comput.
  • 1 September 1996
TLDR
We prove that any graph G of minimum degree at least three contains a dominating set D of size at most 3| V ( G )|/8 vertex disjoint stars. Expand
  • 162
  • 17